| d1 | d2 | Straight | Advantage | Disadvantage |
|---|---|---|---|---|
| 1 | 1 | 1 | 1 | 1 |
| 1 | 2 | 1 | 2 | 1 |
| 1 | 3 | 1 | 3 | 1 |
| 1 | 4 | 1 | 4 | 1 |
| 1 | 5 | 1 | 5 | 1 |
| 1 | 6 | 1 | 6 | 1 |
| 1 | 7 | 1 | 7 | 1 |
Taking Advantage
An Analysis of Advantage/Disadvantage in the D20 System
Mick Cooney mickcooney@gmail.com
Background
Who Am I?
Dublin Data Science
Goals
Test Intuition
Simulate Mechanisms
Illustrate Typical Examples
Setting Up
Discrete space
No need for simulation
\[\begin{eqnarray*} 1d20 &\rightarrow& 20 \text{ possible outcomes} \\ 2d20 &\rightarrow& 400 \text{ possible outcomes} \end{eqnarray*}\]
Create table of outcomes for 2d20.
\[\begin{eqnarray*} \text{Straight: } &\rightarrow& \text{ use first die} \\ \text{Adv/Disadv: } &\rightarrow& \text{ use max/min of two dice} \\ \text{ROLL(P/M)#: } &\rightarrow& \text{ adjust first die} \end{eqnarray*}\]
Analysing Failure
The Champion
Subclass of Fighter
Critical Hit on 19 or 20
What is the impact of advantage / disadvantage
| Roll Type | Target | Success Prob | Failure Prob |
|---|---|---|---|
| Straight | 19 | 0.1000 | 0.9000 |
| Straight | 20 | 0.0500 | 0.9500 |
| Advantage | 19 | 0.1900 | 0.8100 |
| Advantage | 20 | 0.0975 | 0.9025 |
| Disadvantage | 19 | 0.0100 | 0.9900 |
| Disadvantage | 20 | 0.0025 | 0.9975 |
Opposed Rolls
Resolve Contests
Both Roll 1d20, add bonus
Discrete Space
Bigger and messier
Use simulation
Probabilities Comparison
Examples
1st Level Human Fighter vs Orc Warrior
16 STR / Prof (+5 to roll) -> AC 13
Needs 8 or higher on attack roll
| Roll Type | Success | Failure | Failure Ratio |
|---|---|---|---|
| Straight | 0.6500 | 0.3500 | 1.00 |
| Advantage | 0.8775 | 0.1225 | 0.35 |
| Disadvantage | 0.4225 | 0.5775 | 1.65 |
5th Level Half-Orc Fighter vs Peasant
18 STR / Prof (+7 to roll) -> AC 10
Needs 3 or higher on attack roll
| Roll Type | Success | Failure | Failure Ratio |
|---|---|---|---|
| Straight | 0.90 | 0.10 | 1.0 |
| Advantage | 0.99 | 0.01 | 0.1 |
| Disadvantage | 0.81 | 0.19 | 1.9 |
Unskilled Merchant vs Armored Knight with Shield
10 STR / Not proficient (+0 to roll) -> AC 18
Needs 18 or higher on attack roll
| Roll Type | Success | Failure | Failure Ratio |
|---|---|---|---|
| Straight | 0.1500 | 0.8500 | 1.00 |
| Advantage | 0.2775 | 0.7225 | 0.85 |
| Disadvantage | 0.0225 | 0.9775 | 1.15 |
Summary
+/- 3 on average
Non-linearity
Effects non-intuitive
Thank You!
Other Resources
Stand-Up Maths YouTube Channel
This talk…
https://github.com/kaybenleroll/data_workshops/talk_gaming_dndadv_202301